Searing, distinctive voice … Liz White and Michael Malarkey in Tennessee Williams's Spring Storm at the National theatre. Photograph: Robert Day

Long before I became a dedicated follower of theatre, I read plays. I'd come home from the library with handfuls of blue-spined Methuen modern classics, black-spined Penguin volumes of Ibsen and Chekhov, note-spattered editions of Jacobean tragedy and Restoration drama. Yes, I was a weird kid – but I didn't think that my intense engagement with these texts was anything different than with the novels in which I also immersed myself. They were every bit as provoking and personal, and it was great to read the exciting bits aloud.

At first glimpse, the notion seems daft. If Sophocles, Shakespeare and Beckett don't fit a definition of literature, then surely it's the definition that's lacking. But I suspect it's theatre's brazenly collaborative and transient nature that spooks the literary gatekeepers. We may think of the literary experience as essentially solitary: a lone reader's silent encounter with a momentous text. It's a notion freighted with reverence, nudging literature into a secular religiosity. Surely literature isn't – or isn't just – about contemplation, let alone meditation. It's about engagement.

Theatre refuses to deify the lone genius creator. Its rough magic depends on collaboration – from the harmonious to the competing scrabble of hierarchy. Tiffany Stern's new book on early modern theatre argues that what we think of the "the play" is often a baggy compendium of documents: a script (often unreliable), a scenario, a chatter of playbills, prologues and prompter's aids. The surviving printed text may not be the whole story, but that doesn't make it unliterary. It's just not merely literary.

Playwrights are not unused to this disdain. It's no wonder they can become chippy, or seek to fashion their published works into self-consciously literary artefacts. Ben Jonson's vaunting 1616 collection of his works directs the reader's attention towards classical allusion rather than roistering theatricality; Shaw's dialogue famously has to wriggle past screeds of argumentative stage direction. This is drama defiantly presented as literature. Perhaps the closest equivalent might be Alan Bennett's playtexts, prized for their wry forewords as much as their tart and quotable dialogue.

Even if theatre involves a multiplicity of collaborators, that's no barrier to the emergence of a distinctive voice. In Laurie Sansom's inspired revival of Tennessee Williams's barely known student play Spring Storm, currently at the National, the young author's garrulous, witty voice emerges fully fledged, chattering to keep out the dark. It remains a searing, very personal encounter.

Yes, plays change with each production. Rupert Goold makes King Lear a dotty argument about England, Trevor Nunn an operatic lament for humans abandoned by the gods. But novels, too, change with every reader. My cackling, baleful Philip Roth may not be yours; your solemn Iris Murdoch may not be mine. We are mistaken to imagine a work of literature is or should be immutable, sculpted in marble and similarly impervious to change. Literature is one way in which we discover what it is to be human, yet lurking behind this discussion is a peculiar distrust of the human presence. Do bodies and voices compromise a literary work? Is a poem no longer literature if it is read aloud? Or if, like the Odyssey or Beowulf, it was composed for recitation? Even as a playtext, theatre acknowledges flesh and the kinetic thrum of others, on stage and in the auditorium. Plays remind us that literature is warm, mutable and human.